I posted the same question about six months ago and received the same type of replies, with no real answer. However, it did make me think that, yes, that chair probably is quite heavy with the bed mechanism and all in it. I ended up bringing a twin size air matress which fit between the master bed and balcony window. That ended up working pretty good. Perhaps that is a viable option for you.
....and sorry, I also do not know the answer to your original question. Never checked to see if the chair fit through the door but thinking back size-wise, I have a strong suspicion it would not.